The gamma distribution takes two parameters: the shape and the scale. The mean of the distribution will be shape/scale.
That means that for a given mean (pun not intended), there are infinitely many gamma distributions. You'd need to pick either the scale or the shape and then get the other one, given your mean.
Also, the gamma distribution is asymptotic, if you limit it to the 0-1 interval then what you have is a truncated distribution that might be a very bad approximation of the gamma distribution depending on your selected shape and scale parameters.